Class 8 Computational Thinking & AI
Official CBSE Student Handbook curriculum with 110 interactive practice questions, exponential thinking puzzles, quadrilateral spatial proofs, and responsible AI frameworks.
A Square and a Cube
A Square and a Cube develops algorithmic abstraction and algebraic number theory through powers, square/cube number patterns, and constraint satisfaction grids.
Practice Questions (20)
Click an option to test your answerIn the number grid, circles follow a consistent square/cube pattern: • Node 4 → 25 • Node 5 → 106 • Node 3 → 13 • Node 9 → 117 • Node 2 → 85 What will be the value of A + B?
Hint: Analyze the arithmetic operations linking each outer circle to its neighboring grid cells.
Sam writes a list of natural numbers with at most two digits (1 to 99). The list contains exactly three perfect cubes and three perfect squares. What is the MINIMUM number of distinct numbers he must have written?
Hint: Find numbers ≤ 99 that are BOTH a perfect square and a perfect cube (e.g. 1 and 64).
If AB is a two-digit number whose cube is a 4-digit number '__ __ __ C' such that A < C < B, how many different values can C have?
Hint: Two-digit numbers whose cubes have 4 digits are between 10 and 21.
56 × k is a perfect cube where k is a natural number. What is the SMALLEST possible value of k?
Hint: Prime factorize 56 = 2³ × 7¹. What power of 7 is needed to make a complete cube?
Each geometrical shape denotes an operation: • Square[16] → 256 (16²) • Square[19] → 361 (19²) • Cylinder[15] → 3375 (15³) • Cylinder[11] → 1331 (11³) What will come in place of '?' for: Square[14] + Cylinder[12] → ?
Hint: Square means x² and Cylinder means x³. Compute 14² + 12³.
XYZ is a 3-digit number that is the square of a multiple of 5. What is the HIGHEST possible remainder when XYZ is divided by 100?
Hint: The square of any integer ending in 5 always ends in the digits 25.
A pattern on the board shows: • 2³ − 1³ = 1 + 2 × 1 × 3 • 3³ − 2³ = 1 + 3 × 2 × 3 • 4³ − 3³ = 1 + 4 × 3 × 3 For 13³ − 12³, the expression is '1 + 13 × 12 × 3'. Which DIGIT appears the HIGHEST number of times in this expression?
Classroom Board Pattern
2³ − 1³ = 1 + 2 × 1 × 3
3³ − 2³ = 1 + 3 × 2 × 3
4³ − 3³ = 1 + 4 × 3 × 3
Hint: Count the occurrences of each digit in '1 + 13 × 12 × 3'.
Fill a 4×4 grid with squares and cubes of digits 2 to 5 {4, 8, 9, 27, 16, 64, 25, 125} such that: • Each number appears twice • A number's square and cube cannot share a row/column • Identical numbers do not touch diagonally What is the MAXIMUM possible sum of cells in Shape A configuration?
Hint: Place 125 and 64 within the designated cells while satisfying row/column non-overlap.
In a logic machine pipeline: • Row 1: 4 → 15 (4²−1) → 6 → 216 (6³) • Row 2: 22 → 483 (22²−1) → 15 → 3375 (15³) • Row 3: 11 → 120 (11²−1) → 3 → 27 (3³) • Row 4: 7 → A → B → C What is the sum of A, B, and C?
Hint: Column 2 is n² − 1. Column 4 is (Column 3)³.
Every column follows a rule: • CL1: [16, 9 / 12] → √(16 × 9) = 12 • CL2: [28, 7 / 14] → √(28 × 7) = 14 • CL3: [25, 16 / 20] → √(25 × 16) = 20 • CL4: [12, 27 / ?] What number should come in place of '?'
| CL1 | CL2 | CL3 | CL4 |
|---|---|---|---|
| 16 | 28 | 25 | 12 |
| 9 | 7 | 16 | 27 |
| 12 | 14 | 20 | ? |
Hint: Multiply 12 by 27 and take the square root: √(324) = 18.
What is the smallest natural number 'k' such that 3,600 × k is a perfect cube?
Hint: Find the prime factors of 3600 and check which prime powers need supplements to reach the nearest multiple of 3.
The difference between the squares of two consecutive odd integers is always divisible by:
Hint: Use algebraic expansion (2n + 3)² − (2n + 1)².
A solid wooden cube of side 6 cm is painted blue on all 6 faces and then cut into 1 cm unit cubes. How many unit cubes have EXACTLY TWO painted faces?
Hint: Cubes with 2 painted faces are located along the 12 edges minus the corner cubes.
If n² ends with the digit 6, what are the possible units digits of (n + 1)²?
Hint: Determine the units digit of n first when n² ends in 6.
A Pythagorean triplet has 16 as its smallest member. What is the sum of the other two members?
Hint: Apply the Pythagorean triplet formula (2m, m² − 1, m² + 1).
How many non-square natural numbers lie strictly between 45² and 46²?
Hint: Between n² and (n+1)², there are exactly 2n non-perfect squares.
Evaluate the square root: √(1 + 3 + 5 + 7 + ... + 49).
Hint: The sum of the first n odd numbers is n².
What is the smallest number by which 675 must be divided so that the quotient is a perfect cube?
Hint: Factor 675 into prime powers: 3³ × 5².
If x³ = 0.000216, what is the value of (10x)²?
Hint: Find the cube root of 216/1,000,000 first.
A square courtyard of side 32 m is to be paved with square tiles of side 80 cm. How many tiles are required?
Hint: Convert side lengths to centimetres and divide total area by single tile area.
The Thinking Spot: 4-Column Box Stacking
Boxes are stacked in 4 columns A, B, C, and D, each labeled 1, 2, or 3. No two adjacent boxes in the same column share a label. No two adjacent columns share the same topmost number. For every column, the sum of topmost and bottommost numbers is equal.
Question: In the shaded boxes, which number occurs the HIGHEST number of times?